Marcus Rashford proved to be the difference for Manchester United
Against the run of play, Rashford exposed Martin Demichelis and slotted home a composed finish to Joe Hart's left to give United a 1-0 lead.
The goal earned Rashford his place in Red Devils history, making him the youngest ever scorer in a Manchester derby and moved Louis van Gaal's men to within 1 point of the top four.
And Carrick has labelled the goal 'incredible' and heaped praise on his side after a quick turn around from the Europa League defeat to Liverpool in midweek.
"It was a good first half, a great goal from Marcus, an unbelievable finish, he told Sky Sports.
Marcus Rashford - 5 things you need to know
"It has been a tough week. there were bodies cramping out there.
It gives us a real boost, something to go at and momentum for the final stages of the season
Michael Carrick
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"It was a great result and a good way to bounce back from Thursday night. It is more than three points, as it was a must win today.
"It gives us a real boost, something to go at and momentum for the final stages of the season."